Pressure oscillations during wave impact on vertical walls

This paper gives a mathematical description of high frequency pressure oscillations which are observed in measurements of water-wave impacts; particularly impact against a vertical wall. Our ultimate aim is to trace the physical origins of the pressure fluctuations which are related to the understanding of the role of fluid compressibility in breaking wave impact pressure. We investigate possible cases by simplifying the geometry and finding the frequency of free oscillations. We ignore the main flow of water since it has a longer time-scale. Our initial model considers compressible aerated water near the wall and compressible non-aerated water with a much higher sound speed further away. This is compared with a simple example of an air pocket trapped against a wall in incompressible water. Comparisons with three experimental results are encouraging.